HANDBOOK OF TONAL COUNTERPOINT – G. HEUSSENSTAMM – Page 1

CHAPTER ELEVEN CANON IN THREE-PART COUNTERPOINT

Imitation is no stranger to the student who has dwelt among these pages. The

inventions thrive on imitation. And indeed, so do fugues, and to prepare for the kind of

imitation utilizing three parts, we will examine two kinds of canonic writing. The first is

the more difficult and is called a three-part canon, while the second is easier but no

less—perhaps more—important: the accompanied canon.

The THREE-PART CANON. The Leader may appear in any part. The remainng

two parts will be called 1st Follower and 2nd Follower, respectively. The process of

writing a three-part canon is merely an extension of what has been learned regarding

the two-part canon. Write a short, straightforward statement that will be the Leader.

Then copy the statement in the First Follower, as well as the 2nd Follower (if imitation

at the octave is used, be sure that different octave registers are used each time). In order

to start a three-part canon at the octave, we might begin as in the following example:

Then write one measure of continuation in the Leader, forming good

counterpoint with the First Follower. Copy this in the continuation of both First and

Second Follower. The next example shows this process:

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Continue this "leap frog" effect for a short distance, then break the canon and

close with a convincing free cadence. Don't be surprised if you seem to be repeating the

same harmonic progression from measure to measure; this is one of the problems when

writing in imitation at the octave. Try as best you can to maintain fresh melodic interest

as you write each continuation. Notice that there may be gaps wider than an octave

between the upper parts. An extended canon is not necessary. The main thing is to

obtain a grasp of the process and make it work well for a while, then bring the canon to

a close. Here is the final version of the three-part canon at the octave:

Asterisks mark the places where the First and Second Followers break the

imitation as the end of the example nears. Generally, it is unwise to add accidentals in

canons at the octave if those accidentals are not carried out in the followers, but a slight

bit of "cheating" in measure four does enhance the harmonic interest by adding C#'s

(V/V) as seen below. Play the canon with this alteration and you will understand our

meaning.

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Understand that canons are not tolerant of the "change of interval" we allowed

ourselves when writing imitation in inventions. The word canon means "law",

implying strict conformance with the rules. There was no bending of the rules—except

for that possible added interest in measure 4—while the canon was in operation in our

first example. The same will be true henceforth. The interval of imitation is most often

identical between Leader and First Follower and First Follower and Second Follower,

which was an octave in the first example.

Let us experiment now with a different interval of imitation, say at the fifth

above. This will provide much greater variety of harmony, since both of the followers

will have all new pitches. Also, such canons invite the addition of accidentals forming

secondary dominants, possible modulations, etc. Here is a Leader of a three-part canon

at the fifth above, with First and Second Follower at their respective points of imitation:

The next example shows a two-measure continuation of the Leader and its imitation by

the Followers. Since this is a two-measure Leader, all continuations of counterpoint are

written in two-measure segments. Notice the accidentals in measures 3, 5, and 6,

implying momentary secondary dominants. The Leader's structure invites suspensions

and indeed they appear in the realization in both First and Second Follower.

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Remember, caution must be taken to ensure that the canon makes harmonic

sense, that the Leader's line is interesting, and that there is rhythmic differentiation

among the parts. As this short canon proceeds to its conclusion, a few more accidentals

find their place before closing off with an Imperfect Authentic Cadence:

Experimentation with other identical intervals of imitation in three-part canons

will prove rewarding—for instance up a 2nd, where each of the three parts are more or

less the same overall range.

The most difficult form of three-part canon is one in which the intervals of

imitation are not identical. This type of imitative writing was fairly common in 16th

century motets and masses of Palestrina and his contemporaries. Working out such a

canon takes a great deal of extra effort and patience. One example will demonstrate. In

the following canon, notice that the interval of imitation between the Leader and First

Follower is an octave, while the interval of imitation between the First and Second

Follower is a tenth! Acceptable harmonic intervals worked out between Leader and

First Follower may not be acceptable at all between First and Second Follower at

corresponding places in the canon, and there is where the extreme difficulty lies. A 3rd

becomes a 5th, a 6th becomes an octave, etc.

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The Accompanied Canon. Far more usual in three-part counterpoint are two-

part canons with a third free part, the so-called accompanied canons. The supreme

example in all of the literature is Bach's "Goldberg Variations", in which every third

variation is an accompanied canon. These canons proceed in a steadfastly logical way

from, first, a canon at the unison, then a canon at the 2nd, followed by a canon at the

3rd, etc., until a canon at the 9th is reached. In each canon a free third part enriches the

texture, supports the harmony, and coordinates beautifully with the two parts that

constitute the canon. This score is a must for study and analysis.

Very little is new here concerning how to write a canon. The same method as

with two parts is used, except it is possible to have parallel fourths in the upper parts if

the free part is in the bass; consecutive first inversion chords may be brought into the

picture to support the parallel fourths in the upper voices. The further advantage of the

accompanied canon's extra voice is the richer texture, the additional harmonic support,

and the possibility of added rhythmic interest using figures that might be derived from

the two-part canon itself.

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In the following accompanied canon, the upper parts are in canon at the 5th

below. The free lowest part provides solid support. Notice the occasional implicated

secondary dominants:

The next example seems to begin with a canon in contrary motion, but there is no

continuation. The upper parts are in a canon at the third above. The lowest part adds

some related rhythmic figures.

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Following is a final example, Variation No.18 from Bach's Goldberg Variations.

It is an accompanied canon at the 6th above, with only a two-beat Leader. The

accompanying bass part has a prevalent rhythmic figure of a strong beat quarter note

followed by two eighth notes. Further analysis may be seen on the next page.

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As mentioned earlier, this work merits your close attention. The Theme upon

which the variations are constructed is cast in two-part form, with exactly 16 measures

in both Part A and Part B. Accordingly, every one of the Variations is built in precisely

the same manner—16 measures in both parts. As expected from what we have learned

about two-part form, Part A ends with a cadence in the Dominant key—D Major, and in

Part B a move to a closely related key, in this case E Minor, is made before making a full

return to the tonic key of G Major.

In coordination with all of these formal considerations, Bach ingeniously works

in a whole set of accompanied canons (every third variation). In Variation No. 18 there

is a consistent relationship going on between Leader and Follower. Notice the

repetitious nature of measures 1, 5, 9, 13, and 21, always leading off with G in the

Leader and E in the Follower. Bach transposes this pattern to other scale degrees,

especially to C in the Leader and A in the Follower, as in measures 7, 17, 25, and 29.

In terms of extreme economy of material, compare measures 9 through 16 with

measures 25 through 32. Measures 9-16 (in D Major now) are merely transposed up a

perfect 4th back to G Major in measures 25-32, providing a fitting conclusion to the

variation.

Suspensions and tied chord tones abound. Bach also gives us a couple of

sequences: measure 12, beat 2, through measure 14, beat 2, which is repeated starting on

beat 2 of measure 28 through beat 2 of measure 30. Stepwise descending figures are

important, culminating in a ten-note descending scale in measures 10-12 and measures

26-28. There is, in this variation, almost never more than an octave between the upper

parts, but Bach makes extensive use of this freedom in other variations.

We are ready now to undertake the exploration of a three-voice fugue.